Local Isoperimetric Constant Estimate for Integral Ricci Curvature
Presenter
January 15, 2016
Keywords:
- differential geometry
- manifolds
- curvature
- geodesic flow
- Ricci curvature
- L^2 estimates
- heat kernel
MSC:
- 53-xx
- 53Cxx
- 53C05
- 53C07
- 53C15
- 53C22
- 53C44
- 54A20
- 35K08
Abstract
We obtain a local isoperimetric constant estimate for integral Ricci curvature, which enable us to extend several important tools like maximal principle, gradient estimate, heat kernel estimate and $L^2$ Hessian estimate to manifolds with integral Ricci lower bounds, including the collapsed case. This is a joint work with X. Dai and Z. Zhang.